Inverse Matrix

Matrix Inverse

If A is a non-singular square matrix, there is an existence of n x n matrix A-1, which is called the inverse matrix of A such that it satisfies the property:

AA-1 = A-1A = I, where I is the Identity matrix

The identity matrix for the 2 x 2 matrix is given by

It is noted that in order to find the inverse matrix, the square matrix should be non-singular whose determinant value does not equal to zero.

Let us take the square matrix A

Where a, b, c, and d represents the number.

The determinant of the matrix A is written as ad-bc, where the value is not equal to zero. The inverse matrix can be found for 2× 2, 3× 3, …n × n matrices. Finding the inverse of a 3×3 matrix is a bit difficult than finding the inverses of a 2 ×2 matrices.

Inverse Matrix Method

The inverse of a matrix can be found using the following methods:

Method 1:

Similarly, we can find the inverse of a 3×3 matrix by finding the determinant value of the given matrix.